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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 160, Number 1, Pages 102–111
DOI: https://doi.org/10.4213/tmf6382 (Mi tmf6382) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Autoresonant asymptotics in an oscillating system with weak dissipation

L. A. Kalyakina, M. A. Shamsutdinovb

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences
b Bashkir State University
Full-text PDF (451 kB) Citations (16)
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DOI: https://doi.org/10.4213/tmf6382
Abstract: We study a system of two first-order differential equations arising in averaging nonlinear systems over fast single-frequency oscillations. We consider the situation where the original system contains weak dissipative terms. We construct the asymptotic form of a two-parameter solution with an unbounded increasing amplitude. This result gives a key for understanding autoresonance in weak dissipative systems as a phenomenon of significant increase in the forced nonlinear oscillation initiated by a small external pumping.
Keywords: nonlinear equation, perturbation, small parameter, asymptotic behavior, resonance, dissipation.
English version:
Theoretical and Mathematical Physics, 2009, Volume 160, Issue 1, Pages 960–967
DOI: https://doi.org/10.1007/s11232-009-0086-3
Bibliographic databases:
Language: Russian
Citation: L. A. Kalyakin, M. A. Shamsutdinov, “Autoresonant asymptotics in an oscillating system with weak dissipation”, TMF, 160:1 (2009), 102–111; Theoret. and Math. Phys., 160:1 (2009), 960–967
Citation in format AMSBIB
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\paper Autoresonant asymptotics in an~oscillating system with weak dissipation
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\transl
\jour Theoret. and Math. Phys.
\yr 2009
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\issue 1
\pages 960--967
\crossref{https://doi.org/10.1007/s11232-009-0086-3}
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  • https://doi.org/10.4213/tmf6382
  • https://www.mathnet.ru/eng/tmf/v160/i1/p102
    • This publication is cited in the following 16 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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